# cone problems

#### Ellcrys

here are 3 out of 10 questions in my HW.. cant really understand cones..
anyone pls help me?

1. A metal tube 12cm long, with 4cm diameter and 0.5cm thick, is melted and poured into a conical pot with opening diameter of 18cm and 16cm altitude. what should be the depth of the melted metal inside the pot?

2. A glass container initially contains 100 cubic cm. of water. It has a base radius of 2.5cm and the radius of the mouth is 4cm. If the container is 11cm high and is a frustum of a cone, what would be the depth of water inside if 3 ice cubes with 2cm sides are placed inside.

3. A sphere of diameter 1.67 in. rests in a conical wine glass whose semi-vertical angles is 21 degrees. If the glass contains just enough wine to touch the bottom of the sphere, and the quantity of wine in the glass.. (cant really understand this one..)

thanks(Happy)

Ellcrys

#### spruancejr

Question 2:
When dealing with a conical frustum to find volume

$$\displaystyle V = (pi*h/3) (R^2+R*r+r^2)$$

Where h = height, R = lower radius, r = upper radius

Question 3:
Looking at my rough sketch, the black object is the sphere and the red area is the wine that is touching the bottom of the sphere. Is the question asking to find the volume wine in the glass?

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Ellcrys

#### Ellcrys

yeah, he was asking for the volume.. =)

thanks for helping ^_^V